Vol 22, No 2 (2016)

This paper is a brief review of integrable models of gravitation and cosmology in four and more dimensions which make up one of the proper approaches to studying the basic issues and strong field objects, the early and present Universe, and black hole (BH) physics in particular. The main results within this approach, obtained in the recent years by the research group founded by K.P. Staniukovich, are presented. Absolute G measurements and problems of its possible time and range variations, which are reflections of the unification problem, are discussed within these models. The choice, nature, classification and precision of determination of fundamental physical constants and their role in the expected transition to new definitions of basic SI units, supposed to be based on fundamental physical constants and stable quantum phenomena, are described. A need for further absolute measurements of G, its possible range and time variations is stressed. Themultipurpose space project SEE is shortly described, aimed at measuring G and its stability in space and time with a progress of 2–3 orders of magnitude against the present accuracy. It may answer many important questions posed by gravitation, cosmology and unified theories. A project of a laboratory experiment to test possible deviations from Newton’s law of gravity is also presented.

Results on particle creation from vacuum by the gravitational field of the expanding Friedmann Universe are presented. Finite results for the density of particles and the energy density for created particles are given for different exact solutions and different expansion modes of the Universe. The results are obtained for both conformal and nonconformal particles. The hypothesis on the origin of visible matter from the decay of created from vacuum superheavy particles identified with dark matter is discussed.

It is argued that F(R) modified gravity generically leads to high frequency curvature oscillations in astrophysical systems with rising mass/energy density. Potentially observational manifestations of such oscillations are discussed. In particular, gravitational repulsion in finite-size objects, forbidden in standard General Relativity, is shown to exist. Also an alternation of density perturbation evolution is found out. The latter is induced by excitation of a parametric resonance and by the so-called antifriction phenomenon. These new features could lead to strong reshaping of the usual Jeans instability.

The place and physical significance of gauge gravitation theory in Riemann-Cartan spacetime (GTRC) in the framework of the gauge approach to gravitation is discussed. Isotropic cosmology built on the basis of GTRC with a general expression of the gravitational Lagrangian with indefinite parameters is considered. The most important physical consequences connected with a change of the gravitational interaction, with possible existence of limiting energy density and gravitational repulsion at extreme conditions, and also with the vacuum repulsion effect are discussed. A solution of the problem of cosmological singularity and the dark energy problem as a result of the change of the gravitational interaction is considered.

The gravitational D-dimensional model is considered, with l scalar fields, a cosmological constant and several forms. When a cosmological block-diagonal metric, defined on a product of an 1-dimensional interval and n oriented Einstein spaces, is chosen, an electromagnetic composite brane ansatz is adopted, and certain restrictions on the branes are imposed, the conformally covariant Wheeler–DeWitt (WDW) equation for the model is studied. Under certain restrictions, asymptotic solutions to the WDWequation are found in the limit of the formation of billiard walls which reduce the problem to the socalled quantum billiard on (n + l - 1)-dimensional hyperbolic space. Several examples of billiards in the model with {pmn} non-intersecting electric branes, e.g., corresponding to hyperbolic Kac–Moody algebras, are considered. In the classical case, any of these billiards describe a never-ending oscillating behavior of scale factors while approaching to the singularity, which is either spacelike or timelike. For n = 2 the model is completely integrable in the asymptotic regime in the clasical and quantum cases.

The vacuum expectation value of the energy-momentum tensor is investigated for a charged scalar field in dS space-time with toroidally compact spatial dimensions in the presence of a classical constant gauge field. Due to the nontrivial topology, the latter gives rise to an Aharonov-Bohm-like effect on the vacuum characteristics. The vacuum energy density and stresses are even periodic functions of the magnetic flux enclosed by the compact dimensions. For small values of the comoving lengths of the compact dimensions as compared with the dS curvature radius, the effects of gravity on the topological contributions are small, and the expectation values are expressed in terms of the corresponding quantities in the Minkowski bulk by the standard conformal relation. For large values of the comoving lengths, depending on the field mass, two regimes are realized with monotonic and oscillatory damping of the expectation values. We show that the sign of the the vacuum energy density can be controlled by tuning the magnetic flux enclosed by the compact dimensions.

Simultaneous non-configuration geometrization of classical electrodynamics and gravity leads to a 4D space which refer to the Model of Embedded Spaces (MES). MES presupposes the existence of their own space (manifold) in any massive particle (element of matter distribution) and argues that spacetime of the universe is the 4D metric result of dynamical embedding of proper manifolds, whose partial contribution is determined by matter interactions. The resulting space is equipped with Riemann-like geometry, whose differential formalism, in a test particle approximation, is obtained by a formal change of the gradient operator \(\partial /\partial {x^i} \to \partial /\partial {x^i} + 2{u^k}{\partial ^2}/\partial {x^{\left[ i \right.}}\partial {u^{\left. k \right]}}\), where uⁱ = dxⁱ/ds is the velocity of matter. In this paper the features of the geometry of dynamical embedding are analyzed, and MES analogs of the Einstein and Maxwell equations are obtained. It has been shown that the electric charge is a direct consequence of the gravitational constant and inertial mass of matter. We also discuss some fundamental physical and cosmological aspects of the developed ideas.

We consider the well-known Boltzmann brains problem in the framework of simple phantom energy models with little rip and big rip singularities. It is shown that these models (i) satisfy the observational data and (ii) may be free from the Boltzmann brains problem. Human observers in phantom models can exist only during a certain period t < t_f (t_f is the lifetime of the universe) via the Bekenstein bound. If the fraction of unordered observers in this part of the universe history is negligible as comparison with ordered observers, than the Boltzmann brains problem does not appear. The bounds on model parameters derived from such a requirement do not contradict to the allowable range according to the observational data.